Canzani-Garcia, Yaiza
Associate Professor
Phillips Hall 305
canzani@email.unc.edu
Website
Research Interests
Partial differential equations, semiclassical analysis, mathematical physics, quantum mechanics, differential geometry
Professional Background
BS. Universidad de la República, Uruguay, 2008; Ph.D. McGill University, Montreal, 2013; Member of the Institute for Advanced Study, Princeton, 2014-2015; Benjamin Peirce Fellow, Harvard University, Boston, 2013-2016
Research Synopsis
Canzani's research focuses on understanding the behavior of Laplace eigenfunctions, φλ, using techniques of harmonic analysis, spectral theory, geometric analysis, microlocal analysis, probability, and dynamical systems. From a quantum mechanics point of view, |φλ(x)|2 represents the probability for finding a quantum particle of energy λ2 at the point >(x. As a result, understanding how φλ concentrates is a crucial problem for the mathematical physics community. Most of Canzani's research concerns the high energy regime λ→∞.
Representative Publications
Topology and Nesting of the Zero Set Components of Monochromatic Random Waves
Y. Canzani and P. Sarnak.,
Communications on Pure and Applied Mathematics, 72 , 2, 343-374, 2019
On the Growth of Eigenfunction Averages: Microlocalization and Geometry
Y. Canzani and J. Galkowski.,
Duke Mathematical Journal, 168, 16, 2991-3055, 2017
Scaling Limit for the Kernel of the Spectral Projector and Remainder Estimates in the Pointwise Weyl Law
Y. Canzani and B. Hanin.,
Analysis and Partial Differential Equations, 8, 7, 1707-1731, 2015